Gyakuten Saiban games correlate to which Ace Attorney games. This has been especially confusing recently, as Phoenix Wright: Ace Attorney: Trials and Tribulations (based on Gyakuten Saiban 3) was announced for the US at the same time as Gyakuten Saiban 4 was being released in Japan.
4cr must have gotten similar confused comments, but, unlike us, they decided to do something about it. Well, we're doing something about it now, but it's just linking their article, which is much easier. They've written a history of the series, detailing exactly which games were ported from the GBA, and the US and Japanese titles of each game. If this is too academic, you can always buy every lawyery-looking game you see, and figure it out when you get home.